Problem: Rewrite as a simplified fraction. ${0.\overline{84} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 84.8484...\\ 1x &= 0.8484...\end{align*}}$ Subtracting the two equations, we have: ${99x = 84}$ ${x = \dfrac{84}{99}} $ ${x = \dfrac{28}{33}} $